GATE EE 2020 Question Paper (08-Feb-2020) (Shift 1)

x${}_R$ and x${}_A$ are, respectively, the rms and average values of x(t) = x(t - T), and similarly, y${}_R$ and y${}_A$ are, respectively, the rms and average values of y(t) = kx(t), k, T are independent of t. Which of the following is true?

A three-phase cylindrical rotor synchronous generator has a synchronous reactance Xₛ and a negligible armature resistance. The magnitude of per phase terminal voltage is V${}_A$ and the magnitude of per phase induced emf is E${}_A$. Considering the following two statements, P and Q,

P: For any three-phase balanced leading load connected across the terminals of this synchronous generator, V${}_A$ is always more than E${}_A$

Q: For any three-phase balanced lagging load connected across the terminals of this synchronous generator, V${}_A$ is always less than E${}_A$

Which of the following options is correct?

A lossless transmission line with 0.2 pu reactance per phase uniformly distributed along the length of the line, connecting a generator bus to a load bus, is protected up to 80 % of its length by a distance relay placed at the generator bus. The generator terminal voltage is 1 pu. There is no generation at the load bus. The threshold pu current for operation of the distance relay for a solid three phase-to-ground fault on the transmission line is closest to:

Out of the following options, the most relevant information needed to specify the real power (P) at the PV buses in a load flow analysis is

Consider a linear time-invariant system whose input r(t) and output y(t) are related by the following differential equation:

$\frac{d^{2}y\left(t\right)}{d{t}^2}+4y\left(t\right)=6r\left(t\right)$

The poles of this system are at